The left hand side expression of the given equation is a difference of two squares. The first term, x², is a square of x and the second term, 25 is the square of 5. The factors of the expression are (x - 5) and (x + 5).
(x - 5)(x + 5) = 0
The values of x from the equation above are x = -5 and x = 5.
For exponential functions
y=ab^x,
where
a is the scale vertical stretch factor,
b is the base, and
x the exponent (also independent variable)
It is a know fact that if the scale factor (1/2 or 2 in the answer choices) is positive, the graph is increasing if the base (3 or 1/3) is greater than 1.
This means that the base cannot be equal to 1/3. This eliminates choices 3 and 4.
Next, for a base greater than 1 (3>1), and the scale factor positive, it is a dilation (image gets bigger) if the scale factor is greater than 1. This eliminates the first choice where a=2.
This leaves us with the second choice where a=1/2, b=3, which is a shrink of the given exponential base function.
